Remainder and Factor Theorem

Front

What is the Remainder Theorem?

Back

The Remainder Theorem states that the remainder of the division of a polynomial f(x) by a linear divisor (x - c) is equal to f(c).

Front

What is the Factor Theorem?

Back

The Factor Theorem states that a polynomial f(x) has a factor (x - c) if and only if f(c) = 0.

Front

How do you determine if a binomial is a factor of a polynomial?

Back

To determine if (x - c) is a factor of f(x), evaluate f(c). If f(c) = 0, then (x - c) is a factor.

Front

What is the value of p(2) if p(x) = 9x^4 - 45x^3 + 37x^2 + x + 2?

Back

p(2) = -64.

Front

What is the remainder when a^3 - 4 is divided by a + 2?

Back

The remainder is -12.

Front

If f(x) = x^3 + x^2 - 24x + 36, which binomial is a factor?

Back

The factor is x + 6.

Front

What is the first step in using the Remainder Theorem?

Back

The first step is to substitute the value of c into the polynomial f(x).

Front

What does it mean if f(c) = 0?

Back

If f(c) = 0, it means that (x - c) is a factor of the polynomial f(x).

Front

How can you find the remainder of a polynomial division without performing long division?

Back

You can find the remainder by evaluating the polynomial at the value of c from the divisor (x - c).

Front

What is the significance of the Remainder Theorem in polynomial division?

Back

The Remainder Theorem simplifies the process of finding remainders without needing to perform long division.